To such as have never attentively reflected upon this important
subject, it may not readily occur in how great a variety of
modes the knowledge gathered in a properly executed survey of
the coast is instrumental in preserving the seaman from the
disasters to which he is liable. There is no difficulty, indeed,
in understanding how, if the practicable channels are traced
out and marked by buoys, and if the natural landmarks visible
at a distance are accurately mapped down, with their bearings
as observed from point to point, and if artificial beacons are
erected on the headlands, or on the reefs or shoals, a navigator
with the chart before him may be able, in clear weather and
by day, to pick his way in safety by the eye alone. There is
no difficulty in understanding how he may, even on clear nights,
be sufficiently secure in depending upon the guidance of the
beacon-lights of which the survey has fixed the most advantageous
localities. But it is not in the broad light of day, nor yet
when the heavens are serene by night, and the landmarks and
beacons are easily discernible, that ocean disasters occur most
frequently, or take the navigator most usually by surprise.
The moments by far the most perilous are those in which the
solitary voyager is, as it were, walled out from the world by
an impenetrable barrier of mist, limiting the range of his vision,
in every direction, to a distance often not greater than his
own vessel’s length.

In
such a situation of perplexity, helpless as it may appear, the
charts of a perfect coast survey furnish a gauranty of safety,
which, though it exacts of the mariner a more untiring vigilance,
is yet no less to be relied on than the guidance of visible
beacons. The cast of the lead informs of the water beneath him,
and of the nature of the materials which form the bottom encountered
by the plummet. A few successive casts indicate to him the degree
of inclination and the direction of the slope. With these elements
to guide his judgment, he finds his place upon the chart without
difficulty, and traces the line of his progress step by step.
And it is the description of information here indicated which
is most valuable of all to sailors, since this is the only species
which is available when they are in their greatest peril. Yet
it is obvious, without argument, that it is a kind of information
which can only be perfectly gathered by patient, persevering
and long-continued labor; and which, in consequence of the changes
continually going forward in the bed of the sea, can only be
preserved in its accuracy and its value, by frequent and careful
revision.

Another mode in which a scrutinizing examination of the coast
contributes to the safety of navigation is, by the discovery
of sheltered bays or inlets to which vessels may resort in stress
of weather, and where they may lie in safety till the winds
and waves recover their tranquillity. Such harbors of refuge,
as they have been not unaptly called, have been found to exist
in many parts of our extended coast, having been quite unknown
even to the sailors who frequent most the neighboring seas,
until the searching operations of the Coast Survey had brought
them to light. Commerce having failed, for whatever causes,
to appropriate these harbors to its uses, whether on account
of their inconvenient situation in reference to the interior
of the country, or on account of the wildness or sterility of
the surrounding territory, or simply for the reason that their
capabilities had been overlooked; all the benefits which have
flowed from their discovery, all the lives which they have rescued
from destruction, and all the wealth which they have snatched
from the jaws of the deep, are undeniably to be passed, wholly
and entirely, to the credit of this great public enterprise.
And were it possible to strike a balance between the amount
of outlay, on the one hand, by which results of such value and
importance have been accomplished, and the amounts of material
wealth, on the other, which they have redeemed from the waves,
it would unquestionably appear that the sum-total of all the
appropriations which have been made from the public treasury
for the prosecution of the work from the beginning, have been
amply more than overpaid by the benefits which have crowned
some of these, its subordinate and least conspicuous achievements.

But though the leading object contemplated in a survey of the
coast is to provide for the security of navigation, and thus
to subserve the interests of commerce and of humanity, still
there are other important ends incidentally but at the same
time necessarily promoted in the conduct of its operations,
which are too important to be disregarded, and which must be
taken into the account, if we would comprehend the full measure
of the benefits which such a work is capable of conferring upon
mankind. These will be more particularly exhibited in the detailed
account which will presently be given, of the results which
have been already brought out, in the prosecution of our own
Coast Survey. It is sufficient here to state in brief, that
they embrace the accurate determination of favorable bases for
the institution of trigonometrical inland surveys, which may
lead to the construction of scientifically exact maps of the
territory of the several States; of observations on the phenomena
of terrestrial magnetism, and the laws which govern their variations;
of investigations of the difficult problems connected with the
irregularities of the tides and of the winds; of the exploration
of the Gulf Stream and other ocean currents; of the study of
the distribution of submarine deposits by these currents, and
the formation of such deposits near the points of discharge
of the numerous rivers which intersect the coast; of the examination
and settlement of questions relating to suspected or probable
changes of the relative level of land and sea, and other points
of the highest interest to geological science; of the determination
of the sites most advantageous for the construction of national
works of defence, and many other matters of economical or scientific
interest, less general in their character.

METHODS
OF PRACTICE EMPLOYED IN THE CONDUCT OF A GEODETIC AND HYDROGRAPHIC
SURVEY.

Such being the diversified and valuable ends, for the attainment
of which so numerous and elaborate and extensive hydrographic
surveys have been set on foot in modern times, along the coast
lines of our own and of foreign countries, it is consistent
with the design of this report to sketch in outline the methods
of practice which have been employed in the actual execution
of works so magnificent, so truly national in character, so
incalculably useful, and so honorable to the governments which
have undertaken them, and of whose wisdom they are among the
most splendid and enduring moments. The information here embodied
would be unnecessary and out of place, were it to be addressed
to geometers or physicists only: but if the committee rightly
interpret the purpose of the Association in their appointment,
it is a part of their duty to prepare such an account of the
great public work referred to them for review, as may be proper
to lay before the reading public at large.

GEODESY.— With the simple processes involved in ordinary
field surveys, every one may be presumed to be sufficiently
familiar to enable him on a slight consideration to perceive
their insufficiency to determine correctly any considerable
portion of the earth’s surface, or of any long line of
inland or sea-coast boundary. And whoever has reached this point
will find no great difficulty in understanding the general principles
on which the peculiar methods adapted to such extensive works
are founded. In an ordinary survey, the surface of the earth
is regarded as a plane, and every field is considered to be
apart of this plane, bounded by horizontal lines. Now as the
earth is not plane upon its surface, but spherical, it is obvious
that there is error even in the smallest survey executed according
to the ordinary rules. And it is no less obvious that if two
fields, side by side, be independently surveyed, the two planes
supposed to represent them will not be mutually extensions of
each other; but will be slightly inclined to each other, the
angle of their inclination being equal to the amount of the
earth’s curvature between their middle points. In the
case we have just supposed, indeed, this angle would be so very
slight as to be altogether imperceptible: but should we compare
two fields separated from each other by the distance of a hundred
miles, we should find their inclination to be so great, that
the plane of one of them extended in the direction of the other,
instead of coïnciding with it, as it would do if the earth’s
general surface were itself a plane, would pass above it at
the height of a mile and a quarter.

Again, in defining te boundaries of fields, it is necessary
to refer them to certain fixed lines of direction, certain cardinal
points of the horizon, or, as they are commonly called, points
of the compass. Now if the earth were a plane, all the lines
which we call north and south would be parallel to each other;
and so far as the limited space comprehended within a field
or a farm is concerned, such lines are actually sufficiently
near to parallelism for every practical purpose. But since the
earth is spherical, all such lines, wherever drawn, must intersect
each other at last if extend to the poles; and they must consequently
be more or less convergent in every other latitude. The extensive
surveys of the public lands, therefore, executed by the government
surveyors according to the ordinary methods, exhibit but a loose
approximation to correctness; and they have only been preserved
from intolerable inaccuracy, by dividing the territory to be
surveyed into zones limited by parallels of latitude at moderate
distances from each other; and resting each successive zone
upon a new base. To illustrate, by specification, the magnitude
of the error involved in this mode of surveying, when pursued
over long lines or extended surfaces, it may be observed that
such a survey carried from the shore of the Gulf of Mexico to
the northern boundary of the state of Mississippi, would be
erroneous to the extent of four miles in every hundred.

But in a survey designed to represent the features of a coast
with such exactness as to assure safety to the navigator who
depends on the information it affords him, there must be no
question of miles or even of fractions of miles of error; the
rigorous demand is, that there shall be no sensible error at
all. And therefore it is that the methods adopted must recognize,
in the first instance, the fact that the earth is a sphere.
And all the lines and surfaces involved in the various geometrical
and trigonometrical operations, must be reduced to conform to
this fundamental requisition.

But even this does not represent the entire complication of
the task. The results which would be obtained by the strict
application of the processes of spherical geometry and trigonometry
to the glove of the earth considered as perfect in figure, though
immensely nearer to the truth than any that could be reached
by plane trigonometry alone, would still fail to exhibit the
points of the earth’s surface as nature has presented
them. For the earth after al is not a perfect sphere; but is
larger in equatorial than in polar diameter by about twenty-six
miles. It is this deviation from the truly globular shape which
makes of the earth what is called an oblate spheroid; and this
must still be allowed for, before a survey like that which we
are considering can possess the accuracy that either science
requires, or the safety of navigation demands.

To a survey of this kind is applied the term, geodetic. Having
indicated the nature of the geometrical principles upon which
its determinations rest, it may be proper to give a brief account
of the instrumental methods which are employed in the field,
in gathering the data for these determinations. The first step,
which is to serve as the basis of all subsequent operations
is, to measure with extreme accuracy, in a convenient and level
spot, a base line of several miles in length. And when we speak
of accuracy, it is to be observed that the word as here use
is to be received in a much more several rigorous sense than
is the case in its ordinary applications. By the methods in
practice in the American Coast Survey, a line ten miles long
may be measured with no greater error than a fraction of an
inch.

After this first very delicate but mainly mechanical process
has been completed, the next thing to be done is to fix upon
some prominently conspicuous and conveniently distant point,
visible from both extremities of the base, and forming with
them, by imaginary aerial lines, a triangle of large dimensions.
All the angles of this triangle are then very carefully measured
with instruments of the nicest accuracy; and from the values
thus obtained and the known length of the measured base, the
length of the unknown aerial sides is determine by trigonometrical
computation.

Each of these unknown sides having become now known, may in
its turn be made the base of a new aerial triangle; its extremities
furnishing two of the angular points, and some new station still
more distant, and falling conveniently in with the plan of the
survey, supplying the third. Thus, by the continued repetition
of the process here described, a chain of triangles is constructed
step by step, which follows generally the windings of the coast,
but extends also as far inland as may be necessary to obtain
for the triangles the dimensions most favorable to accuracy.
For it need hardly be remarked that, if there be minute errors
committed in the instrumental parts of the work, as is doubtless
unavoidable even when instruments possess the extremest delicacy
which art in its highest refinements has been able to secure,
these, though singly imperceptible, may grow by repetition and
accumulation, until error actually sensible begins to vitiate
the results. On this account, therefore, it is desirable that
the instrumental measurements should be as few as possible:
and accordingly, in this principal chain of distances, the triangulation
points are chosen as far from each other as the nature of the
country will admit. It is a consequent necessity that the network
of triangulation, in order that it may fulfil every important
condition, should occupy a band of considerable breadth along
the coast. Indeed, some of the lines which form the sides of
these aerial triangles, are not less than seventy miles in length:
yet it is entirely demonstrable that the accumulated total of
all the error with which they are vitiated, does not exceed
a single foot.

As a check upon errors of this description, and as a means of
testing the precision with which the instrumental and numerical
processes have been conducted along an extended line of triangulation,
new bases, called bases of verification, are occasionally measured,
often some hundreds of miles distant from the original base;
and the length as trigonometrically computed through the whole
chain, is compared with that which is found by actual measurement.
So close has, in many instances, been the agreement between
results obtained by methods so widely different, as almost to
exceed belief. A base of verification measured in France, in
connection with the triangulation carried on through that kingdom
for the determination of the length of a degree of the meridian,
differed less than a foot from the value found for the same
base, by computation through a chain of triangles, four hundred
miles long. A similar base upwards of seven miles in length,
measured on Salisbury Plain, in England, showed less than a
single inch of disagreement with the result deduced by calculation
from an original base at the distance of one hundred miles.
The American Survey furnishes an example no less remarkable.
A base five and a half miles long on an island in Chesapeake
bay, as actually measured, and as determined through a triangulation
of more than three hundred miles, presents results discordant
to the extent of only four inches.